Finite Group DatabasebetaFinite Group Databasebeta| order | 28420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(Dic145⋊C7) |
| unambiguous semidirect product | Dic1015⋊C7 |
| derived | C5×C7×C29 ⋊ C4×C7 |
| Hall | C5×C7×C29⋊C7 ⋊ C4 |
| Hall | C7×C29⋊C7 ⋊ Dic5 |
| Hall | C5×C29 ⋊ C7×Dic7 |
| Sylow | C29 ⋊ C7×Dic35 |
| Sylow | C5 ⋊ C7⋊(Dic29⋊C7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(C7⋊(D29⋊C7)) |
| commutator, hypocenter | C5×C7×C29 | C4×C7 |
| Fitting, socle, cosocle | C2×C5×C7×C29 | C2×C7 |
| prime radical | C2×C5×C7×C29⋊C7 | C2 |
| LCS | G ▷ C5×C7×C29 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4060 |
Polycyclic presentation:
2,7,5,7,29,2|a^2=f,c^a=c^4,d^a=d^6,e^a=e^28,e^b=e^16406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28420, 57);